The aim of this paper is to investigate whether the Euro-US dollar exchange rate cointegrates with other major exchange rates since the introduction of the Euro. In order to evaluate whether the introduction of a new currency, which has commonly replaced more and less established currencies, has generated common stochastic trends which are possibly linked to cross-inefficient markets, the results are compared with those of a cointegration analysis of the pre-Euro era. We can show that after the introduction of the Euro two cointegration relationships arise among the Euro-US dollar and the four most important exchange rates, whereas the no-arbitrage condition is satisfied. Here, we discovered a new result: free floating exchange rates are cointegrated after the introduction of the Euro. The Euro-US dollar exchange rate cointegrates with the Australian dollar-US dollar and with the British pound-US dollar. In both cases the Euro-US dollar is weakly exogenous. The results coincide with comovements of important fundamentals which imply cross-market efficiency.